EDM Report on the Chi-Chi, Taiwan Earthquake of September 21, 1999

89

5. Simulation of Damage Process

Numerical analyses were carried out to understand the damage process of port facility and buildings duringthe earthquake. In section 5.1, the damage process of the caisson-type quaywall in Taichung Harbor was analyzedby using the 2-dimensional dynamic effective stress method. We discussed the extent of liquefaction behind thequaywall and the permanent movement of the quaywall. In section 5.2, a high-rise RC apartment building is usedto investigate the damage process and mechanism when subjected to the near fault acceleration records in differentlevel of PGA. Three-dimensional frame model considering the nonlinear behavior of individual structuralmembers is used in the analysis to calculate the building's responses to the ground motions.

5.1 Quaywall in Taichung Harbor

During the 1999 Chi-Chi Earthquake, the Taichung Harbor was partially damaged. The caisson quaywallsmoved seaward and the unloading facilities were damaged at the Piers No.1 to No.4A located beside the NorthDocking Channel. These damages were considered to be due to liquefaction of reclaimed sand, because manysand boils were observed behind the quaywalls. Liquefaction analysis of the soil-structure system was performedto understand the damage process during the earthquake.

5.1.1 Damaged Quaywall in Taichung Harbor

In Taichung Harbor, remarkable damages were observed at the North terminal only. Damage descriptionabout Taichung Harbor has already been made in section 2.5, therefore a brief description about the damage ismade here. Structural conditions of quaywalls and soil conditions of backfill are especially described here.

Figure 5.1.1 shows a typical cross section of Pier No.1 to No.3 of Taichung Harbor (Chen and Hwang, 2000).Each pier consists of ten caissons. Each concrete caisson has four cells, with a height of 19.6 m and a width of 17.6m. These quaywalls at Pier No.1 to No.4 were designed by the �Design Manual of Harbor Structures in Japan1967� (Japan Society of Civil Engineers, 1999). The design seismic coefficient is 0.15 for all caissons. Thequaywalls were constructed as follows; 1) excavation of the foundation, 2) construction of layers of cobbles andboulders, 3) installation of the RC caissons and filling the backfill cobbles and boulders. The ground behind the

Figure 5.1.1. Typical cross section of Pier No.1 to No.3 of Taichung Harbor (Chen and Hwang, 2000).

Chapter 5. Simulation of Damage Process

90

quaywalls was hydraulically filled with sands dredged from the sea, then a gravel of thickness 30 cm and asphaltpavement was layered.

Figure 5.1.2 shows a schematic section of soil profiles near Pier No.3 in the North terminal, which is basedon the results of geological boring logs performed after the earthquake (Chen and Hwang, 2000). The originalseabed consists mainly of sands of loose to medium dense, interbedded with several thin layers of clayey silt orsilty clay. SPT-N values of the seabed range over about 20. The averaged SPT-N value from GL-20m to GL-40m was about 25 based on the in-situ tests at Pier No.1 (Japan Society of Civil Engineers, 1999). Above theoriginal seabed, sands dredged from the navigation channel and nearby areas are filled hydraulically to the presentground level. The hydraulic sand fills consist of mainly fine sands. The sand fills are quite loose, and theirSPT-N values range from 5 to 14 (Chen and Hwang, 2000). Therefore, the hydraulic sand fills under the watertable could be liquefied during the earthquake.

Ground failures and structural damage observed in the investigated area are concluded as shown in Figure2.5.2. Many sand boils were observed at several sites mainly around the ground depressions and the verticalgaps occurred between the caissons and backfill soils. The backfill soils subsided due to seaward movementsand inclinations of the caissons (Photo. 2.5.1), and length and width of the subsided area were about 800 m and 40m, respectively. Most of the caissons were damaged slightly or not. Maximum values of inclinations andhorizontal displacements of the caissons were about 1-3 degree and 1.7 m, respectively as shown in Figures 2.5.3.Maximum settlement of backfill soils was about 1.4 m as shown in Figures 2.5.4. The deformed configuration

Figure 5.1.2. Soil profiles along the cross section of Pier No.3 (Chen and Hwang, 2000).

Figure 5.1.3. Damaged configuration of the caisson in Pier No.2 (Center of Harbor and Marine Technology, 1999).

Chapter 5. Simulation of Damage Process

91

of the caisson at Pier No.2 was measured by the Center of Harbor and Marine Technology as shown in Figure5.1.3 (Center of Harbor and Marine Technology, 1999). The top surface of the caisson experienced a horizontaldisplacement of 80cm and a tilt angle of 1 degree. It was estimated that the foundation of the caisson will have ahorizontal displacement of 50cm.

5.1.2 Numerical Method

Governing Equations

In this study, the governing equations of for the coupling problems between soil skeleton and pore waterwere obtained with the two phase mixture theory (Biot, 1962). Using a u-p (displacement of the solid phase -pore water pressure) formulation (Zienkiewicz and Bettes, 1982), a simple and practical numerical method for thetwo-dimensional liquefaction analysis was formulated. The finite element method (FEM) has been usually usedfor the spatial discretization of the governing equations. In this study, however, the finite element method (FEM)was used for the spatial discretization of the equilibrium equation, while the finite difference method (FDM) wasused for the spatial discretization of the pore water pressure in the continuity equation (Akai and Tamura, 1978).The accuracy of the proposed numerical method was verified by Oka et al. (1994) through a comparison ofnumerical results and analytical solutions for transient response of saturated porous solids. As details of thismethod were given in Oka et al. (1994), only a brief description of the method is given below. The governingequations are formulated by the following assumptions; 1) the infinitesimal strain, 2) the smooth distribution ofporosity in the soil, 3) the small relative acceleration of the fluid phase to that of the solid phase compared with theacceleration of the solid phase, 4) incompressible grain particles in the soil. The equilibrium equation for themixture is derived as follows:

ijijsi bu ρσρ += ,�� (5.1.1)

where ρ is the overall density, siu is the acceleration of the solid, ijσ is the total stress tensor and ib is the

body force. The continuity equation is derived as follows:

0, =+−− pkKn

kp f

wsii

wii

sii

f����

γεγερ (5.1.2)

where fρ is the density of the fluid, p is the pore water pressure, wγ is the unit weight of the fluid, k is thecoefficient of permeability, s

iiε is the volumetric strain of the solid, n is porosity and fK is the bulk modulus ofthe fluid.

Constitutive Models

The constitutive equation used for sand is a cyclic elasto-plastic model (Oka et al., 1992, Tateishi et al., 1995).The constitutive equation is formulated by the following assumptions; 1) the infinitesimal strain, 2) the elasto-plastic theory, 3) the non-associated flow rule, 4) the concept of the overconsolidated boundary surface, 5) the non-linear kinematic hardening rule. The performance of the constitutive model was verified by Tateishi et al. (1995).The model succeeded in reproducing the experimental results well under various stress conditions, such asisotropic and anisotropic consolidated conditions, with and without the initial shear stress conditions, principalstress axis rotation, etc.

5.1.3 Numerical Conditions

The quaywall of Pier No.2 was selected for this study, because its backfill area is an open space without anystructures. Figure 5.1.4 shows the 2-dimensional FE model made from the typical cross section as shown in

Chapter 5. Simulation of Damage Process

92

Figure 5.1.1. The depth of the model was determined to be EL �33m, because SPT-N value was over 50 at thedepth according to the in-situ tests at Pier No.1 (Japan Society of Civil Engineers, 1999). The width of the modelwas set to be enough wide, considering the liquefiable sand fill area as shown in Figure 5.1.2.

We applied the cyclic elasto-plastic model for sand to all soil materials, which were backfill sand, originalseabed, backfill rubble and foundation rubble. The model parameters are divided to two categories, basicparameters and fitting parameters. The basic parameters, density, internal friction angle, initial shear moduluswere normally determined by the in-situ tests and laboratory tests using undisturbed. These basic parameterswere derived from the static stability analysis of the caisson (Chen and Hwang, 2000). The initial shear moduleswere estimated from the mean SPT-value, which were 10 in the backfill sand and 25 in the original seabed. Thefitting parameters were determined by adjusting technique. For the backfill sand, the parameter values wereselected by trial and error in order to describe the liquefaction strength curve. The liquefaction strength curveswere estimated from the mean SPT-N value by using the method of Japanese Highway Bridge Specification(Japan Road Association, 1996). The cyclic shear stress ratio of backfill sand, required to cause 5% axial strainin 20 cycles, was about 0.22. For other soils, which were original seabed, backfill rubble and foundation rubble,dilatancy effect was neglected and nonlinear characteristic of shear deformation was only taken into account.

The concrete caisson quaywall was modeled by linear elastic elements. The slip between the caisson andrubble was modeled by joint elements whose parameters were derived from the static stability analysis of thecaisson (Chen and Hwang, 2000). The friction factors were 0.50 on the foundation rubble and 0.27 on thebackfill rubble. The initial stress state was computed by the static elasto-perfectly-plastic analysis, in which theDrucker-Prager type failure surface model was employed.

In Taiwan, an intense strong motion array called TSMIP has been installed island-wide. Near TaichungHarbor, there are several seismograph stations in near distance. Among them, the closest one is the stationlocated at the Elementary School of Chigshui (Station Code: TCU059, on ground), where is about 4.7 kmsoutheast of the Harbor. During the main shock of the earthquake, the accelerations of ground motions at the sitewere successfully recorded and are available tentatively (Lee et al., 1999). Figure 5.1.5 (a) and (b) show theacceleration time series of the two orthogonal horizontal motions (EW and NS components) recorded at TCU059.Peak ground accelerations (PGA) of the both motions are about 160 gal. The input motion for the analysis asshown in Figure 5.1.5 (c) was corrected to N6.5E of the direction of analytical model section. The correctedmotion was input from the viscous bottom boundary of the FE model. The time integration step of 0.001 wasadopted, and the simulation was performed for 72 seconds. The Rayleigh damping proportional to initial stiffnesswas used to reproduce the damping in high frequency domain.

70 62.2

17.6

70

17.0

5

EL. -13.00m

EL. +6.20mEL. +1.90m

Caisson

Backfill sand

Seabed soil

Seabed soilBackfill rubble

Foundation rubble

Viscous boundary

Free fieldboundary

Free fieldboundary

(Unit :m)

Figure 5.1.4. FE model for Pier No.2 of Taichung Harbor (Refer to color figure 7).

Chapter 5. Simulation of Damage Process

93

5.1.4 Numerical Results

Figure 5.1.6 (a) shows the distribution of excess pore water pressure ratio after the earthquake. Completeliquefaction occurred in the backfill sandy layer, which agreed with the observation of many sand boils at thebackfill sand. Few excess pore water pressure occurred in the seabed and rubbles, because dilatancy effect wasneglected in these layers. Figure 5.1.6 (b) shows the deformed configuration after the earthquake and the amountof displacement at the top of the caisson. The scale of deformation is the same as that of the FEM mesh and thearrows in the figure shows the direction of the magnitude of displacement. The simulation reproduced a horizontaldisplacement of about 0.80 m at the top of the caisson, which agreed with the measured displacement of about0.80 m in Pier No.2 as shown in Figure 5.1.3. On the other hand, the vertical displacement at the top of thecaisson was about 0.41 m, which was larger than the measured displacement of about 0.18 m in Pier No.2 asshown in Figure 5.1.3. The predicted mode of deformation of the caisson agreed with the measured one asshown in Figure 5.1.3. The deformation of the caisson was due to the increased lateral pressure of the backfillliquefied soils and deformation of foundation rubble and seabed soil. According to the measured configurationof the caisson as shown in Figure 5.1.3, the caisson seems to move seaward with slip at the bottom. However,Little slip between the foundation rubble and the caisson bottom occurred in the predicted deformed configuration,

-200

-100

0

100

200

0 10 20 30 40 50 60 70 80

EW, TCU059

Acc

eler

atio

n (G

al)

Time(s)

(a) EW component

-200

-100

0

100

200

0 10 20 30 40 50 60 70 80

NS, TCU059

Acc

eler

atio

n (G

al)

Time(s)

(b) NS component

-200

-100

0

100

200

0 10 20 30 40 50 60 70 80

Corrected, N6.5E

Acc

eler

atio

n (G

al)

Time(s)

(c) Input motion

Figure 5.1.5. Acceleration records at TCU059 (Lee et al., 1999) and input motion.

Chapter 5. Simulation of Damage Process

94

although the backfill rubble slightly slipped along the caisson wall. We had better need further investigationabout model parameters for the slip joint elements and foundation seabed soils.

5.1.5 Summary

Liquefaction analysis of the soil-structure system was performed to understand the damage process of thecaisson quaywall in Taichung Harbor during the earthquake. We discussed the extent of liquefaction behind thequaywall and the permanent movement of the quaywall. The numerical simulation reproduced liquefaction ofbackfill sand and seaward deformation of the caisson quaywall. For more accurate prediction, we had betterneed further investigation about soil parameters especially about the foundation seabed soils.

Acknowledgements

The authors are grateful to Mr. Ming-Tuh Hsieh of Research Center of Harbor and Marine Technolog, for hisvaluable comments about the construction of caisson quaywalls in Taichung Harbor.

0.80

0.41

0.0 0.5 1.0

(b) Deformed configuration after earthquake

u/σ'v0

(a) Distribution of excess pore water pressure ratio

: After earthquake : Before earthquake

Deformation scale / Mesh scale = 1.0

: Displacement (m)

Figure 5.1.6. Numerical results (Refer to color figure 8).

Chapter 5. Simulation of Damage Process

95

References

Akai, K. and Tamura, T. (1978), �Study of two-dimensional consolidation accompanied by an elasto-plasticconstitutive equation�, Proc. of JSCE, No.269, pp.98-104. (in Japanese)

Biot, M. A. (1962), �Mechanics of deformation and acoustic propagation in porous media�, Journal of AppliedPhysics, 33, 4, pp.1482-1498.

Center of Harbor and Marine Technology (1999), �Preliminary investigations for the damage of pier #1 to #4A ofTaichung Harbor during the 921 earthquake,� Report No.172, Center of Harbor and Marine Technology,Institute of Transportation, Ministry of Transportation and Communications, ROC.

Chen, H. C. and Hwang, G. S. (2000), �Preliminary analysis for quay wall movement in Taichung Harbor duringthe September 21, 1999, Chi-Chi- Earthquake,� Earthquake Engineering and Engineering Seismology,Special Issue for 921 Chi-Chi Earthquake, Chinese Taiwan Society for Earthquake Engineering, Vol. 2, 1,pp.43-54.

Japan Road Association (1996), �Specifications for Highway Bridges, Part V: Seismic Design,� pp.91-94.

Japan Society of Civil Engineers (1999), �The 1999 Ji-Ji Earthquake, Taiwan, - Investigation into damage to civilengineering structures - ,� pp.5-1 - 5-10.

Lee, W. H. K., T. C. Shin, K. W. Kuo, and K. C. Chen (1999), �CWB free-field strong-motion data from the 921Chi-Chi Earthquake,� Volume 1, Digital Acceleration Files on CD-ROM, Pre-Publication Version(December 6, 1999), Seismology Center, Central Weather Bureau, Taipei, Taiwan.

Oka, F., Yashima, A., Kato, M. and Sekiguchi, K. (1992), �A constitutive model for sand based on the non-linearkinematic hardening rule and its application�, Proc. 10th World Conf. on Earthquake Engineering, Barcelona,pp.2529-2534.

Oka, F., Yashima, A., Shibata, T., Kato, M., and Uzuoka, R. (1994), �FEM-FDM coupled liquefaction analysis ofa porous soil using an elasto-plastic model�, Applied Scientific Research, 52, pp.209-245.

Tateishi, A., Taguchi, Y., Oka, F. and Yashima, A. (1995), �A cyclic elasto-plastic model for sand and itsapplication under various stress conditions�, Proc. 1st Int. Sym. on Earthquake Geotechnical Engineering,IS-TOKYO�95, pp.399-404.

Zienkiewicz, O. C. and Bettes, P. (1982), �Soils and other saturated media under transient, dynamic conditions.General formulation and the validity of various simplifying assumptions�, Soil Mechanics-Transient andCyclic Loads, New York, John Wiley & Sons, pp.1-16.